The massless thermal field and the thermal fermion bosonization in two dimensions

TL;DR

This paper revisits fermion bosonization in two dimensions, introducing a new approach for steady states with different temperatures for left and right movers, and provides applications including a derivation and an operator solution.

Contribution

It presents a novel construction for bosonization in steady states with temperature differences, emphasizing infrared states and their role in correlation functions.

Findings

Derived a new formula in the free relativistic case.

Provided a full operator solution for the massless Thirring model.

Linked infrared states to the behavior of correlation functions.

Abstract

We come back to the issue of bosonization of fermions in two spacetime dimension and give a new costruction in the steady state case where left and right moving particles can coexist at two different temperatures. A crucial role in our construction is played by translation invariant infrared states and the corresponding field operators which are naturally linked to the infrared behaviour of the correlation functions. We present two applications: a simple new derivation in the free relativistic case of a formula by Bernard and Doyon and a full operator solution of the massless Thirring model in the steady state case where the left and right movers have two distinct temperatures.